Cartesian three-dimensional method to quantify displacements between cone beam computed tomography models

ABSTRACT Introduction: Research in Orthodontics and Oral Surgery has been relying on three-dimensional (3D) models to evaluate treatment results with displacement color map techniques, even though it has important limitations. Objectives: This study proposed a method of tracking translational movements of 3D objects to evaluate displacements in surfaces with no shape modification. Methods: Cone Beam Computed Tomography (CBCT) data of ten patients were imported to the Dolphin software. A hypothetical virtual surgical plan (randomly defined) was developed in the software and afterwards verified using the proposed method. All the procedures were carried out by two evaluators, in two different time-points, with a 15-day interval. ITK-Snap software was used to generate high quality STL models. Centroid points were automatically generated and their coordinates were compared to confirm if they represented the known displacements simulated. The paired t-test and the Bland-Altman plots were used, as well as the intraclass correlation coefficient. Results: Interexaminers and intra-examiner tests showed excellent reliability of the method, with mean displacement measurement error values under 0.1mm. The paired t-test did not show any statistically significant differences. Conclusion: The method showed excellent reliability to track the simulated translational displacements of bone segments.


INTRODUCTION
The gold standard for the orientation and comparison of different tomographic time points is the voxel-based computed tomography superposition, introduced in Dentistry by Cevidanes et al. 1 This method uses the existing grayscale differences in voxels to perform the alignment of two images, without the need to rely on operator landmark placement. 2 Before the assessment is performed, it is necessary to segment the tomographic model to be studied, generating a reliable three-dimensional (3D) model in Standard Triangle Language (stl). For this procedure, semi-automatic segmentation is the gold standard. When it comes to the quantification of differences among these superimposed models, the commonly used methods are: anatomical landmarks comparisons, color maps and shape correspondence. Furthermore, these methods present deficiencies that may influence the reliability and/or practicality of the analysis. 3 The first 3D image evaluations used anatomical landmarks comparisons, as often used to track changes in Orthodontics when analyzing two-dimensional images. Linear and angular measurements to describe surface changes have also been widely Dental Press J Orthod. 2022;27(5):e222199 Casagrande CPM, Casagrande MVS, Teixeira AOB, Alencar DS, Dias BSB, Almeida RCC, Quintão CA, Carvalho FAR -Cartesian three-dimensional method to quantify displacements between cone beam computed tomography models 5 used since the pioneer studies using 3D tomographic models.
However, landmark placement is critical for both methods, requiring calibrated evaluators to produce accurate measurements. 3 Color maps became a popular method of comparing 3D models. This quantification method plots, graphically, the distances between homologous points on the surfaces of models to be compared. Although this technique intuitively illustrates regional changes, and software tools allow the user to measure the mean point distances of a given area, its major drawback is that homologous points are usually determined by Iterative Closest Point (ICP) algorithm, which uses the smallest point-to-point distance between two surface models, and frequently results in an incorrect correspondence between anatomical structures. This issue is even more evident when the evaluated anatomical structures present marked curvature areas, as the mandible. Furthermore, it is not possible to assess the direction of changes. 4 Trying to overcome this issue, the shape correspondence method was developed to evaluate virtual 3D surface models, mapping similar structures and identifying correspondent anatomical points using the first order ellipsoid from the spher- Casagrande CPM, Casagrande MVS, Teixeira AOB, Alencar DS, Dias BSB, Almeida RCC, Quintão CA, Carvalho FAR -Cartesian three-dimensional method to quantify displacements between cone beam computed tomography models 6 This method is reliable and overcomes the limitations of the ICP, although it lacks a proper graphical user interface (GUI) and is extremely time-consuming, which constrains its routine application. 5 Thus, due to the limitations of the existing methods, the present study aimed at describing and validating a novel and efficient methodology for tracking translational (vertical, sagittal and transversal) displacements between 3D models of anatomical regions. The used value of 0.4mm represents commonly used voxel size (full-head CBCT scans), so that differences smaller than this are considered intrinsic to the CBCT evaluation.  (Table 1) for the three planes of space (sagittal -X-axis; vertical -Y-axis; transversal -Z-axis) using the iOS random 1.1 application (Mireia Lluch Ortola). There was no concern in obtaining an ideal occlusal result (Fig 1), while all HVSP aimed to represent as far as possible the range of surgical movements, respecting the limits described by Proffit's discrepancy envelope. At the end of this process, .stl files of the maxillary and mandibular segments (initial and post-HVSP) of each patient were exported. This step was performed in Dolphin imaging software and aimed to test if the proposed method could be used to verify the simulated surgery values.

Creation of an accurate 3D model -3D models produced
by Dolphin ® are good enough for visualization purposes and to determine the bone fragments spatial position, but are not accurate enough to represent the exact shape of a bone segment, since the 3D model generation is based simply on limited voxel intensity thresholding (Fig 2A). The creation of the best possible 3D models can be achieved by the semi-automatic CBCT segmentation. 9 Therefore, it was used the semi-automatic segmentation procedures in ITK-SNAP software (Cognitica, Philadelphia, Pa), which utilizes active contour methods to compute anatomic structures based on the CBCT image gray level intensity and boundaries. In this way, accurate surface models of the regions of interest were also exported as .stl files.
Steps 4 to 7 comprise the actual methodology proposed and tested on this study, and will be necessary whenever it is used to track 3D objects translations.

Aligning models -Geomagic Qualify 2013 (3D Systems, Rock
Hill, SC) was used to align (best fit) the reliable surface models generated by the ITK-SNAP software (v. 3.6; Cognitica, Philadelphia, Pato) to the less precise Dolphin models (used as a spatial reference). From this point on, the ITK models oriented according to their Dolphin counterparts were used as the models to be evaluated (Fig 2). To assess this superimposition, the RMS (root mean square) was analyzed.  in Figure 4 illustrates the procedures step by step. The paired t-test was used to compare the known displacements created by the HVSP, and the translations measured by the proposed method. The Bland-Altman plots were also used to compare the mean differences between both methods.

RESULTS
Mean differences between the known HVSP and the translational displacements measured by the proposed method showed discrepancies smaller than 0.1mm for all evaluated situations (for both examiners) (Tables 2 and 3). The paired t-test did not show any statistically significant differences (Tables 2 and 3).

Intraclass correlation coefficients revealed excellent intra-and
inter-examiner reproducibility, and the mean difference and confidence interval showed values smaller than 1 mm ( Casagrande CPM, Casagrande MVS, Teixeira AOB, Alencar DS, Dias BSB, Almeida RCC, Quintão CA, Carvalho FAR -Cartesian three-dimensional method to quantify displacements between cone beam computed tomography models 16 Table 2: Descriptive statistics and paired t-test comparing the differences between the VSP performed in Dolphin and the method using centroid, found by Evaluator 1, considering the displacement direction.  The Bland-Altman graphics were used to illustrate the differences between the methods recorded by evaluator 1. In the maxilla, it was observed that for sagittal and vertical movements the mean difference was -0.05 mm (Fig 5, 1X, 1Y).
For those two directions, nine out of ten values were very close to the average, and one was an outlier. For transversal movements (Fig 5, 1Z) the mean difference was 0.03 mm.
For the mandible, the mean differences were: 0.01 mm for sagittal movements (Fig 5, 2X); 0.06 mm for vertical movements (Fig 5, 2Y) and 0.04 mm for transversal movements (Fig 5, 2Z). Even the outliers values were smaller than 1 mm, which are very close to the spatial resolutions of CBCT used in the present study (Fig 5, 1 and 2).
In Bland-Altman plots, used to determine intra and inter-examiners reproducibility, it can be seen that the 95% limit of agreement does not exceed 0.7mm, showing an excellent result. The "Z" axis showed a greater difference, in comparison with the "X" and "Y" axes, between examiners 1 and 2.
In another hand, the "Y" axis showed a greater difference between two-time points for examiner 1. To check the quality of superimposition, the RMS (root mean square) was used to assess the differences in positioning between the models (Dolphin and ITK). The RMS corresponds to the absolute average of the distances in a normalized way. The RMS found is 0.22 ± 0.12 (mean and standard deviation of RMS, in mm), showing that both models were properly superimposed.

DISCUSSION
Automatic or semiautomatic CBCT segmentation is key in order to build reliable 3D models. [2][3][4] Quantitative evaluations should be translational or rotational, based on the different axes (X, Y, and Z). 2 In this research, a surgical simulation was performed with the Dolphin Imaging ® VSP module, due to its marketing popularity and availability, as well as the author's proficiency with this software. An important drawback of the Dolphin, however, is that although the created 3D model precisely represents the anatomical spatial position, it does not accurately represent its shape. To overcome this limitation, all the quantifications carried out in this study were based on semiautomatic seg- Using two models from different origins, in the present study, represented that it was necessary to align the .stl files from different sources, despite the fact that the same CBCT scans were used for segmentation, in both software. As the quality of those files generated with Dolphin was lower, this could add imprecision to their alignment with the ITK's models, which could contribute to an increase in the differences between the simulated and the measured values. However, the results obtained showed that these changes were not relevant, and the method proved to be reliable. The shape correspondence method is now the gold standard in the evaluation of morphological changes due to pathological processes, growth changes, and skeletal displacements.
The method described in this study is limited when compared to the shape correspondence, due to the impossibility to verify displacements in structures that would undergo shape On the other hand, although shape correspondence is freely available through the SPHARM-PDM toolbox, it lacks a proper graphical user interface (GUI), and its workflow is extremely time-consuming, therefore limiting its broader application. 5,10 Considering the application of this method in a real-world environment of a pre-versus post-surgical sample, it could be suitable for nongrowing individuals if the anatomical regions of interest did not suffer any morphological changes; for instance, in a mandibular advancement surgery, the overall shape of the mandible is altered by the procedure, but the subregions like the chin or the condyles keep their shape in the short term. Caution should be taken in order to use the current method for longer follow-ups. There is a lack of evidence that the ROIs are morphologically stable in the long term.
Some studies tried to access translational changes decomposing displacements on different axes of space, 11,12 but the methodologies used were dependent on the operator for landmark placement, which incorporates errors in the measurements.
In addition, the studies that evaluated the clinical results produced by existing VSP software, analyzed tomographic images of patients who underwent orthognathic surgery. 10,12 Their results could be considered biased, since the surgical In Bland-Altman plots, between examiner 1 and 2, although the difference in Z axis was greater than on the X and Y axis, this difference remained small, with an average of -0.18mm.
In another hand, the "Y" axis showed a greater difference between two-time points in examiner 1. This was due to the measurements of a patient that had a greater variation.
Despite this, the differences remained small. for this determination, such as the use of facial landmarks, 13 systems of algorithms to calculate the rotations of objects, or laser scanners, 14 all of these methods present some validation problem, in addition to variations in cost and practicality. 13 The use of the 3D centroid in this study is advantageous when compared to manual landmark placement, since it is automat- is not ideal. 11,[15][16][17][18][19] Even in a case when a centroid was used, it was based on a triangle determined by the vertices, which were manually defined. 17 A limitation of the centroid point is that it does not allow evaluation of rotational movements.
In this study, the mean error was less than 0.1 mm. Even the extreme errors, represented by the outliers, were smaller than 1 mm, which is very close to the spatial resolution of the CBCT (0.7 mm), 6 and below the clinically relevant limit, com- Furthermore, a study that evaluates rotational movements could be associated with this method, to run a complete 3D evaluation.

CONCLUSION
Although the proposed method requires three different software to be performed, it proved to be accurate and not dependent on the operator's calibration. This may be a useful method for tracking translational displacements of 3D structures in a reliable way. Developers could compile the needed tools in a single software in the future, making the workflow more user-friendly and thus stimulating its use by both clinicians and researchers.